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Time to stationarity for general Markov fluid models
Author(s) -
Nabli Hédi
Publication year - 2006
Publication title -
international journal of communication systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.344
H-Index - 49
eISSN - 1099-1131
pISSN - 1074-5351
DOI - 10.1002/dac.747
Subject(s) - uniformization (probability theory) , computer science , transient (computer programming) , markov chain , upper and lower bounds , simple (philosophy) , markov process , expression (computer science) , flow (mathematics) , buffer (optical fiber) , mathematics , transient analysis , fluid queue , transient flow , steady state (chemistry) , markov model , mathematical optimization , markov property , queueing theory , statistics , mathematical analysis , philosophy , computer network , chemistry , operating system , telecommunications , geometry , epistemology , machine learning , programming language
In this paper, we analyse the buffer content behaviour for general Markov fluid models. Departing from a uniformization‐based solution in transient regime, we deduce the steady‐state buffer content distribution and we give a simple expression measuring a time to stationarity. Moreover, for a fixed period of time, an upper bound for the absolute difference between the transient solution and the asymptotic one is proposed. As an application example, a heterogeneous fluid‐flow model is considered and analysed with our proposed method. Copyright © 2005 John Wiley & Sons, Ltd.
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